Show that B = {x^2, (x -1)^2, (x + 1)^2}is a basis for P2
I'm not even sure how to do this, so any help would be great!
Well, the equation exhibited in post # 2 has to hold for all values of x. If you plug in those three values, one at a time, you get three fairly simple equations for the three unknowns. Then you can solve for them. And, assuming you get even one solution, you will have proven what you need to prove.
Substitution, or elimination is probably the best way to go.